– (This representative point is
usually the centre of mass.)
11
Describing motion(1.Motion Diagrams,
2.Graphs,
3. Equations);
Position and displacement; Velocity; Acceleration; Free Fall
•
Reference Frames
:
– The motion of a physical object is
always described within a certain
frame of reference. Your
coordinate
axes
are defined with respect to a
certain origin.
–
Laboratory frame
(often: x pos. to the
left, y pos. up.) Starting positions and
times are often set to zero: x
i
= x
0
= 0
m and t
i
= t
0
= 0 s.
– Choice of reference frames
important for accelerating objects
(e.g., elevators, trains,...) or objects
moving relative to each other.
12
Describing motion(1.Motion Diagrams,2.Graphs,
3.Equations
);
Position and displacement; Velocity; Acceleration; Free Fall
3. Equations:
–
Equations involving quantities with well defined
meanings such as
velocity, acceleration, displacement,
mass…
– Equations are precise and allow to predict the outcome
of experiments.
5
13
Describing motion(1.Motion Diagrams,2.Graphs,
3.Equations
);
Position and displacement; Velocity; Acceleration; Free Fall
•
Displacement:
Vector pointing from the initial to
the final position:

vector
(“Net distance traveled with direction”.)
•
Average Speed
: Distance traveled in time t.
v = distance/time

scalar
•
Average Velocity
:
v = displacement/time

vector
• Acceleration
:
a = velocity/time

vector
i
f
r
r
r
−
=
Δ
14
Describing motion(1.Motion
Diagrams,2.Graphs,
3.Equations
); Position and
displacement; Velocity; Acceleration; Free Fall
Vectors and Scalars
:
•When a physical quantity is described by a single number
we
call it a scalar.
•In contrast a vector has both a
magnitude
and
direction
in
space.
•Vector notation
•Magnitude of vector
or
A
A
r
A
r
15
Describing motion(1.Motion Diagrams,2.Graphs,3.Equations);
Position and displacement
; Velocity; Acceleration; Free Fall
•
Mathematically, we describe the motion of an
object as follows:
– Call the initial position x
i
(at a time t
i
)
– Call the final position x
f
(at a later time t
f
> t
i
)
– The displacement is given by
Δ
x = x
f
– x
i
•
You may obtain a negative displacement such as
Δ
x =  1.7 m. What does it mean?
•
Important: Displacement is
not equal
to the
distance traveled. Why?
6
16
Question
•
A ball is tossed vertically upwards and after
reaching a max. height of 3.0 m, it falls to the
floor. The ball comes to rest exactly 1.0 m below
its starting position. If x is positive upwards, what
is the displacement of the ball?
A) 1.0 m
B) 7.0 m
C) 3.0 m
D)  1.0 m
E)  7.0 m
17
Question
•
A ball is tossed vertically upwards and after
reaching a max. height of 3.0 m, it falls to the
floor. The ball comes to rest exactly 1.0 m below
its starting position. What is the total distance
traveled?
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 Spring '09
 Lioudmila
 Acceleration, Velocity, Vavg